If they are freshly painted maybe they could leak and evidently harm your fish. If its harmful for humans and animas to ingest, imagine what it could do to a fish's gills andtheir tank. I have no idea, but i would definitelynot submerge anything that isn't fish-safe into your tank that isn't dry yet.

Once its dry though with a topcoat, it should be fine. I put my nails in the tank with no problems, just make sure its dry :)

I used to be rather hesitant to paint my nails because my hands were always in tanks doing one thing or another......but the past three months or so I've had my nails painted almost constantly and haven't had any sort of problems. I'm, of course, very careful to paint at least a day before water change day to let my nails dry thoroughly and wash my hands a couple of times and whatnot, but so far no issues.
I think, like MyRainbowBettaFish said, so long as you're not sticking freshly painted/wet nails in the tank you're fine xD

Do you use topcoat? I would just make sure to do that and always wait 2 hours between nail painting and fish aquarium fiddling. It'll protect your fish from whatever is in the polish (clear has got to be better than tiny flakes of glitter or neon orange or what have you) and keep the polish from chipping.

And just a general FYI in case anyone wants to know, acrylic nails are notorious for trapping/spreading harmful bacteria. They would not mix well with fish tank submersion.

They're definitely not going to be harmful.....not that many toxins can leech out in that time, and even if they do, it wouldn't be very harmful to the fish. Now, leaving a dried glob of around the size of a quarter in there for an hour would definitely leech, but for now you're alright!